Player of a video game is confronted with a series of opponents and has a 80% probability of defeating each one. Success with any opponent is in dependant of any previous encounters and the player continues to contest opponents until defeated.
a) What is the probability mass function of the number of opponents in a game?
b) What is the probability that a player defeats at least two opponents in a game?
c) What is the expected number of opponents contested in a game?
d) What is the probability that a player contests four or more opponents in a game?
e) What is the expected number of game plays until a player contests four or more opponents?